Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems

DOI10.4208/NMTMA.2014.1320NMzbMATH Open1324.65137arXiv1307.7543OpenAlexW2950248683WikidataQ128347319 ScholiaQ128347319MaRDI QIDQ5260342

Sebastian Franz, Hans-Goerg Roos

Publication date: 29 June 2015

Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)

Abstract: In this paper we present a first supercloseness analysis for higher-order Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using a solution decomposition and a special representation of our finite element space we are able to prove a supercloseness property of order p+1/4 in the energy norm where the polynomial order p>=3 is odd.

Full work available at URL: https://arxiv.org/abs/1307.7543

zbMATH Keywords

singular perturbationconvection-diffusion problemGalerkin finite element methodsuperconvergencepostprocessinglayer-adapted meshessupercloseness

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (6)

Supercloseness of the continuous interior penalty method for singularly perturbed problems in 1D: vertex-cell interpolation ⋮ Superconvergence analysis and PPR recovery of arbitrary order edge elements for Maxwell's equations ⋮ Uniform supercloseness of Galerkin finite element method for convection-diffusion problems with characteristic layers ⋮ A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time ⋮ Superconvergence analysis of high-order rectangular edge elements for time-harmonic Maxwell's equations ⋮ Superconvergence in high-order Galerkin finite element methods

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